1=2x^2-11x

Solution for 1=2x^2-11x equation:

1=2x^2-11x

We move all terms to the left:

1-(2x^2-11x)=0

We get rid of parentheses

-2x^2+11x+1=0

a = -2; b = 11; c = +1;
Δ = b2-4ac
Δ = 112-4·(-2)·1
Δ = 129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{129}}{2*-2}=\frac{-11-\sqrt{129}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{129}}{2*-2}=\frac{-11+\sqrt{129}}{-4}
$